outline of the lectures lecture 1: the einstein equivalence principle lecture 2: post-newtonian...
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Outline of the LecturesOutline of the Lectures
Lecture 1: The Einstein Equivalence PrincipleLecture 2: Post-Newtonian Limit of GRLecture 3: The Parametrized Post-Newtonian FrameworkLecture 4: Tests of the PPN Parameters
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Outline of the LecturesOutline of the Lectures
Lecture 1: The Einstein Equivalence PrincipleLecture 2: Post-Newtonian Limit of GRLecture 3: The Parametrized Post-Newtonian FrameworkLecture 4: Tests of the PPN Parameters
Deflection of light Shapiro time delay Perihelion advance Nordtvedt effect and lunar laser ranging Gyroscope precession & Gravity Probe B LAGEOS tracking Tests of the Strong Equivalence Principle Summary of bounds on the PPN Parameters
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Light Bending and Alternative Gravitation TheoriesLight Bending and Alternative Gravitation Theories
Deflection =
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12 (1+ γ )1".7505 /d
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a + ′ b + ′ c = 180o
a + b + c = 180o − γ (0".875 /d)
SpaceCurvature
GR=1
Cavendish 1784von Soldner 1803Einstein 1911
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v → c
a
b’ c’
b c
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The parameter (1+The parameter (1+)/2)/2
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Measuring light deflection using VLBIMeasuring light deflection using VLBI
541 quasars1977-199987 VLBI sites1.7 million measurement
S. S. Shapiro et al (2004)
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ai = −mx i
r31− (2γ + 2β )
m
r+ γv 2 − (2 + α 1 − 2ς 2)
μ
r
⎡ ⎣ ⎢
+ 12 (6 + α 1 + α 2 + α 3)
μ
mv 2 − 3
2 (1+ α 2)μ
m(v ⋅ ˆ n )2 ⎤
⎦ ⎥
+m(x ⋅v)v i
r3(2γ + 2) −
μ
m(2 −α 1 + α 2)
⎡ ⎣ ⎢
⎤ ⎦ ⎥
m = m1 + m2 μ = m1m2 /m
PPN Equation of motion for a binary systemPPN Equation of motion for a binary system
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Mercury’s Perihelion: from Trouble to TriumphMercury’s Perihelion: from Trouble to Triumph
• 1687 Newtonian triumph
• 1859 Leverrier’s conundrum
• 1900 A turn-of-the century crisis
575 “percentury
Cause Rate (per century)
Venus 278 ‘’
Earth 90 ‘’Jupiter 154 ‘’
Others 10 ‘’
Total 532 ‘’
Discrepancy 43 ‘’
Modern value 42.98 + 0.04 ‘’GR Prediction 42.98 ‘’
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Tests of the Weak Equivalence PrincipleTests of the Weak Equivalence Principle
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GRAVITY PROBE BGRAVITY PROBE B
Goal 0.4 mas/yrLaunch April 20, 2004
Mission ended Sept 2005
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Gravity Probe B: The Experiment -- Payload
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Gravity Probe B: The Experiment -- GyroscopesGravity Probe B: The Experiment -- Gyroscopes
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Parameter Effect or Experiment Bound Remarks
- 1Time delay 2.3 X 10-5 Cassini tracking
Light deflection 4 X 10-4 VLBI
- 1Perihelion shift 3 X 10-3 J2 = 2 X 10-7
Nordtvedt effect 2.3 X 10-4 LLR, < 3 X 10-4
Earth tides 10-3 gravimeters
Orbit polarization10-4 LLR
2 X 10-4 J2317+1439
Spin precession 4 X 10-7 Sun axis
Self-acceleration 4 X 10-20 Pulsar spindown
-- 2 X 10-2 Combined bounds
Binary acceleration 4 X 10-5 PSR 1913+16
Newton’s 3rd law 10-8 Lunar acceleration
-- Not independent
Bounds on the PPN ParametersBounds on the PPN Parameters
=4-y-3-10/3-1+22/3-21/3-2/3
Bound on scalar-tensor gravity: > 40,000